In this paper, we present a theory of tensor products of classes of modules for a vertex
operator algebra. We focus on motivating and explaining new structures and results in this …

0. Introduction. The category of finite direct sums of standard (integrable highest weight)
modules of a fixed positive integral level k for an affine Lie algebra ˆg is particularly …

We describe a logarithmic tensor product theory for certain module categories for a"
conformal vertex algebra". In this theory, which is a natural, although intricate, generalization …

In conformal field theory, intertwining operators (or chiral vertex operators) are very
important and useful tools. For rational conformal field theories many important concepts …

The theory of vertex operator algebras is a remarkably rich new mathematical field which
captures the algebraic content of conformal field theory in physics. Ideas leading up to this …

We generalize the tensor product theory for modules for a vertex operator algebra previously
developed in a series of papers by the first two authors to suitable module categories for …

In contrast with the finite dimensional case, one of the distinguished features in the theory of
infinite dimensional Lie algebras is the modular invariance of the characters of certain …

The notion of vertex operator algebra arises naturally in the vertex operator construction of
the Monster--the largest sporadic finite simple group. From another perspective, the theory of …

Introduction. The first construction of the integrablehighest-weight representations of affine
Lie algebras or loop algebras by Kac iK] was greatly inspired by the generalization of the …

This is the first part in a series of papers in which we introduce and develop a natural,
general tensor category theory for suitable module categories for a vertex (operator) …